NCERT Solutions Ganita Prakash (Part 2) Chapter 5 Mean and Median with Frequencies — In-text Questions
Book page 110 Updated on2026-09-05
Q1.
What is the average family size of students in your class? How would you find this out?
Answer
Collect the data first, then use a frequency table rather than a long list.
Ask every student how many members there are in their family and note each answer.
Make a table of family size against how many students gave that answer — this is the frequency.
Multiply each family size by its frequency, add these products to get the total number of family members counted.
Divide by the total number of students.
Average family size = (sum of all the values) ÷ (number of values)
= Σ(family size × frequency) ÷ Σ(frequency)
Tip: the frequency table is not just tidier — it is what stops you from adding each family size only once when several students gave the same answer.
Q2.
What is the average family size of this class?
Answer
5.22 members — not 6.5.
Family size
3
4
5
6
7
8
9
10
Frequency
3
11
9
7
3
1
1
1
size × frequency
9
44
45
42
21
8
9
10
Total number of students = 3 + 11 + 9 + 7 + 3 + 1 + 1 + 1 = 36
Total of all family sizes = 9 + 44 + 45 + 42 + 21 + 8 + 9 + 10 = 188
Average = 188 ÷ 36 = 5.22
Why 6.5 is wrong: (3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) ÷ 8 = 6.5 averages the eight different sizes, as though one student had each. But eleven students have a family of 4 and only one has a family of 10. The mean must count 4 eleven times over. Because the common sizes are the small ones, the true average is pulled well below 6.5.
Q3.
What is the median family size of this class?
Answer
5 members.
There are 36 values, so the median is the average of the 18th and 19th values in order.
Running (cumulative) totals:
up to 3: 3 → positions 1–3
up to 4: 3 + 11 = 14 → positions 4–14
up to 5: 14 + 9 = 23 → positions 15–23
The 18th and 19th values both fall in that block, so both are 5.
Median = (5 + 5) ÷ 2 = 5
Mean 5.22 but median 5: the mean is dragged slightly up by the few large families (8, 9 and 10 members), while the median simply reports where the middle student stands and ignores how large those families are.
Q4.
Do we need to write all the 36 numbers in order? Is there a quicker way to find out?
Answer
No — the frequency table already holds the order. Add the frequencies from the smallest value upwards until you pass the middle position.
Family size
Frequency
Cumulative frequency
Positions it occupies
3
3
3
1 to 3
4
11
14
4 to 14
5
9
23
15 to 23
6
7
30
24 to 30
7
3
33
31 to 33
8
1
34
34
9
1
35
35
10
1
36
36
Positions 18 and 19 lie in the row for 5, so the median is 5 — found without writing a single one of the 36 numbers.
Tip: the cumulative frequency column answers “how many students have a family of this size or smaller?”. Once you can read positions off it, finding a median in data of any size becomes a matter of one column of additions.